A method for controlling a chemical reactor such as a gas-phase reactor using a non-linear predictive control includes steps for generating a plurality of signals representing a current state of the chemical reactor and reflecting a respective constituent of reactants in the chemical reactor, calculating a future state of the chemical reactor responsive to said plurality of signals and referenced to mass hold-up of the reactants in the chemical reactor, and controlling at least one parameter related to the chemical reactor so as to control the future state of the chemical reactor. Spurious control events due to noise in sensor or controller output signals are preferably minimized by filtering these signals using a N-sign filter subroutine.
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1. A method for generating a filtered signal from a plurality of raw signals and at least one previously generated filtered signal, the method comprising steps for: (a) calculating n FACTOR values according the expressions: ##EQU17## (b) calculating n f values according to the expressions: EQU fn=SIGN[X(t)-Xf(t-n)]*FACTORn EQU fn-1=SIGN[X(t-1)-Xf(t-n)]*FACTORn-1 ##EQU18## (c) calculating fsum according to the expression: EQU fsum=ABS(f1+f2+f3+ . . . +fn) (d) calculating FAC according to the expression: EQU FAC=([ABS(fsum)]/n).sup.z (e) calculating the smoothed value XS(t) according to the expression: EQU XS(t)=(a0)X(t)+(a1)X(t-1)+ . . . +(an-1)X(t-(n-1)); and (f) calculating a filtered value Xf(t) according to the expression (60): EQU Xf(t)=Xf(t-1)+FIL*FAC*{XS(t)-Xf(t-1)}, wherein: X(t) =raw data point at time t; Xf(t)=filtered signal at time t; n is a positive integer; z is a positive number; and 1=a0+a1+ . . . +an-1.
2. The method according to claim 1, wherein n is equal to 3.
3. The method according to claim 2, wherein said steps (a)-(f) collectively perform the following algorithm: EQU f3=SIGN[X(t)-Xf(t-3)]*1.0 EQU f2=SIGN[X(t-1)-Xf(t-3)]*1.0 EQU f1=SIGN[X(t-2)-Xf(t-3)]*1.0 EQU fsum=f1+f2+f3 EQU FAC=(ABS(fsum)/3).sup.z EQU XS(t)=[X(t)+X(t-1)+X(t-2)]/3 EQU Xf(t)=Xf(t-1)+FIL*FAC*{XS(t)-Xf(t-1)}.
4. The method according to claim 1, wherein n is equal to 4 and wherein said steps (a)-(f) collectively perform the following algorithm: ##EQU19## f4=SIGN[X(t)-Xf(t-4)]*FACTOR4 EQU f3=SIGN[X(t-1)-Xf(t-4)]*FACTOR3 EQU f2=SIGN[X(t-2)-Xf(t-4)]*FACTOR2 EQU f1=SIGN[X(t-3)-Xf(t-4)]*FACTOR1 EQU fsum=ABS(f1+f2+f3+f4) EQU FAC=([ABS(fsum)]/4).sup.z EQU XS(t)=[X(t)+X(t-1)+X(t-2)+X(t-3)]/4 EQU Xf(t)=Xf(t-1)+FIL*FAC*{XS(t)-Xf(t-1)}.
5. The method according to claim 1, wherein n is equal to 5 and wherein said steps collectively perform an algorithm: ##EQU20## f5=SIGN[X(t)-Xf(t-5)]FACTOR5 EQU f4=SIGN[X(t-1)-Xf(t-5)]*FACTOR4 EQU f3=SIGN[X(t-2)-Xf(t-5)]*FACTOR3 EQU f2=SIGN[X(t-3)-Xf(t-5)]*FACTOR2 EQU f1=SIGN[X(t-4)-Xf(t-5)]*FACTOR1 EQU fsum=INT(ABS(f1+f2+f3+f4+f5)) EQU FAC=([ABS(fsum)]/5).sup.z EQU XS(t)=[X(t)+X(t-1)+X(t-2)+X(t-3)+X(t-4)]/5 and EQU Xf(t)=Xf(t-1)+FIL*FAC*{XS(t)-Xf(t-1)}.
6. A numerical filter generating a filtered signal from a plurality of raw signals and at least one previously generated filtered signal, comprising: first means for calculating n FACTOR values according the expressions: ##EQU21## second means for calculating n f values according to the expressions: EQU fn=SIGN[X(t)-Xf(t-n)]*FACTORn EQU fn-1=SIGN[X(t-1)-Xf(t-n)]FACTORn-1 ##EQU22## third means for calculating fsum according to the expression: EQU fsum=ABS(f+f2+f3+ . . . +fn) fourth means for calculating FAC according to the expression: EQU FAC=([ABS(fsum)]/n).sup.z fifth means for calculating the smoothed value XS(t) according to the expression: EQU XS(t)=(a0)X(t)+(a1)X(t-1)+ . . . +(an-1)X(t-(n-1)); and sixth means for calculating a filtered value Xf(t) according to the expression (60): EQU Xf(t)=Xf(t-1)+FIL*FAC*{XS(t)-Xf(t-1), wherein: X(t)=raw data point at time t; Xf(t)=filtered signal at time t; n is a positive integer; z is a positive number; and 1=a0+a1+ . . . +an-1.
7. The numerical filter as recited in claim 6, wherein n is greater than or equal to 2.
8. A numerical filter generating a filtered signal from a plurality of raw signals and at least one previously generated filtered signal, comprising: first means for calculating n FACTOR values according the expressions: ##EQU23## second means for calculating n f values according to the expressions: EQU fn=SIGN[X(t)-Xf(t-n)]*FACTORn EQU fn-1=SIGN[X(t-1)-Xf(t-n)]*FACTORn-1 ##EQU24## third means for calculating fsum according to the expression: EQU fsum=INT(ABS(f1+f2+f3+ . . . +fn)) fourth means for calculating FAC according to the expression: EQU FAC=(ABS(fsum)/n).sup.z fifth means for calculating the smoothed value XS(t) according to the expression: EQU XS(t)=(a0)X(t)+(a1)X(t-1)+ . . . +(an-1)X(t-(n-1)); and sixth means for calculating a filtered value Xf(t) according to the expression (60): EQU Xf(t)=Xf(t-1)+FIL*FAC*{XS(t)-Xf(t-1), wherein: X(t)=raw data point at time t; Xf(t)=filtered signal at time t; n is a positive integer; z is a positive number; and 1=a0+a1+ . . . +an-1.
9. The numerical filter as recited in claim 8, wherein n is greater than or equal to 2.
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June 7, 2000
July 17, 2001
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